Consequently the quartic \(Q(x,v)\)  is presented as a sum of the fourth-order powers of the components of the vector \(v\) . The first and the second-order derivatives of such expression evidently vanish on the corresponding axes, see Appendix A. 2 for explicit formulas. Due to Eq.(REF ), the determinant of Finsler's metric vanishes on every axis of the vector space separately.
It means that for a vector \(v\)  lying on the axis there is another vector \(u\)  which norm relative to \(v\)  is zero, \(|u|_v=0\) .
This problem is well-known, see e.g. [1]}. It can be solved by extension of the basic definition of Finsler's structure by the sub-additivity axiom.
